SECT. 1.] TO POSITION IN THE ORBIT. 21 



But the Barkerian is by far the most convenient, and is also annexed to the 

 admirable work of the celebrated OLBERS, (Abhandlung uber die leichtcste und 

 bequemste Methodc die Bahn eines Cometen zu lerechnen: Weimar, 1797.) It contains, 

 under the title of the mean motion, the value of the expression 75 tan i v -\- 25 

 tan 3 i v, for all true anomalies for every five minutes from to 180. If 

 therefore the time corresponding to the true anomaly v is required, it will be 



necessary to divide the mean motion, taken from the table with the arguments, 



150 k 

 by 5-, which quantity is called the mean daily motion; if on the contrary the 



P* 



true anomaly is to be computed from the time, the latter expressed in days will 



be multiplied by - , in order to get the mean motion, with which the correspond- 



P* 

 ing anomaly may be taken from the table. It is further evident that the same 



mean motion and time taken negatively correspond to the negative value of the v ; 

 the same table therefore answers equally for negative and positive anomalies. If 

 in the place of jo,we prefer to use the perihelion distance bp = q, the mean daily 



motion is expressed by ~ - -, in which the constant factor ^y/ 2812.5 = 



9 b 

 0.912279061, and its logarithm is 9.9601277069. The anomaly v being found, 



the radius vector will be determined by means of the formula already given, 



20. 



By the differentiation of the equation 



tan i v -\- I tan 8 %v = 

 if all the quantities v, t, p, are regarded as variable, we have 



Stk 



rr 



